Hilbert Transform
in [Matlab]
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From: David Egger on 7 May 2008 02:33 Hey, I unterstand the algorithm hilbert.m in Matlab. But can anyone tell me: 1)Is this the ideal Hilbert or an approximation? 2)Who invented the algorithm? 3)do anyone know a book where I can find the alg.? Regards!
From: Andy Robb on 7 May 2008 06:09 "David Egger" <eggerd(a)sbox.tugraz.at> wrote in message <fvriev$b1i$1(a)fred.mathworks.com>... > Hey, > > > I unterstand the algorithm hilbert.m in Matlab. > But can anyone tell me: > > 1)Is this the ideal Hilbert or an approximation? > 2)Who invented the algorithm? > 3)do anyone know a book where I can find the alg.? > > Regards! I spent many years applying Hilbert transforms, often combining them with re-sampling techniques (Shannon et al). There are two approaches to the Hilbert transform. Both synthesise an imaginary component of a complex analytic waveform from the 'real' signal. The real component should be unchanged. From memory, hilbert.m uses an FFT approach, it zeros frequency components below 0 and double frequency components between zero and Nyquist. The IFFT then produces a complex analytic waveform. The problems with this approach are the same as any FFT technique and can suffer the effects of truncation. An alternative approach is to synthesise the imaginary component directly from the real component using a time-domain filter. From my dim and distant pass, I think you can see the shape of an FIR by synthesising a spectrum with 1i in positive frequencies and -1i in negative frequencies and zero in all real components (including 0 and Nyquist). Then take the IFFT.
From: Doug Schwarz on 7 May 2008 08:13 In article <fvrv3v$8ja$1(a)fred.mathworks.com>, "Andy Robb" <ajrobb(a)hotmail.com> wrote: > "David Egger" <eggerd(a)sbox.tugraz.at> wrote in message > <fvriev$b1i$1(a)fred.mathworks.com>... > > Hey, > > > > > > I unterstand the algorithm hilbert.m in Matlab. > > But can anyone tell me: > > > > 1)Is this the ideal Hilbert or an approximation? > > 2)Who invented the algorithm? > > 3)do anyone know a book where I can find the alg.? > > > > Regards! > > I spent many years applying Hilbert transforms, often > combining them with re-sampling techniques (Shannon et al). > > There are two approaches to the Hilbert transform. Both > synthesise an imaginary component of a complex analytic > waveform from the 'real' signal. The real component should > be unchanged. > > From memory, hilbert.m uses an FFT approach, it zeros > frequency components below 0 and double frequency components > between zero and Nyquist. The IFFT then produces a complex > analytic waveform. The problems with this approach are the > same as any FFT technique and can suffer the effects of > truncation. > > An alternative approach is to synthesise the imaginary > component directly from the real component using a > time-domain filter. From my dim and distant pass, I think > you can see the shape of an FIR by synthesising a spectrum > with 1i in positive frequencies and -1i in negative > frequencies and zero in all real components (including 0 and > Nyquist). Then take the IFFT. The functions firls and firpm from the Signal Processing Toolbox can be used to synthesize the imaginary component. See the help for those functions. -- Doug Schwarz dmschwarz&ieee,org Make obvious changes to get real email address.
From: David Egger on 7 May 2008 08:45 "Andy Robb" <ajrobb(a)hotmail.com> wrote in message <fvrv3v$8ja$1(a)fred.mathworks.com>... > "David Egger" <eggerd(a)sbox.tugraz.at> wrote in message > <fvriev$b1i$1(a)fred.mathworks.com>... > > > From memory, hilbert.m uses an FFT approach, it zeros > frequency components below 0 and double frequency components > between zero and Nyquist. The IFFT then produces a complex > analytic waveform. The problems with this approach are the > same as any FFT technique and can suffer the effects of > truncation. --------------------------------------------------------- Hey, thank you for answering! Okay, I want to keep the algorithm based on the manipulation in the frequency domain you explained. Do you know who invented this algorithm? You said, it is an approach.So this is not an ideal filter? Is an ideal Hilbert filter possible? You also said,the problem with this approach are the same as in any fft approach.Could you name some of them? Regards!
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